Apollonius <Pergaeus>, Apollonii Pergaei Conicorvm Lib. V. VI. VII. paraphraste Abalphato Asphahanensi : nunc primum editi ; additvs in calce Archimedis assvmptorvm liber, ex codibvs arabicis mss Abrahamus Ecchellensis Maronita latinos reddidit, Jo. Alfonsvs Borellvs curam in geometricis versione contulit & [et] notas vberiores in vniuersum opus adiecit

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[Item 1.]
[2.] APOLLONII PERGÆI CONICORVM LIB. V. VI. VII. & ARCHIMEDIS ASVMPTOR VM LIBER.
[3.] APOLLONII PERGÆI CONICORVM LIB. V. VI. VII. PARAPHRASTE ABALPHATO ASPHAHANENSI
[4.] ADDITVS IN CALCE ARCHIMEDIS ASSVMPTORVM LIBER, EX CODICIBVS ARABICIS M.SS. SERENISSIMI MAGNI DVCIS ETRVRIÆ ABRAHAMVS ECCHELLENSIS MARONITA
[5.] IO: ALFONSVS BORELLVS
[6.] AD SERENISSIMVM COSMVM III. ETRVRIÆ PRINCIPEM FLORENTIÆ, Ex Typographia Ioſephi Cocchini ad inſigne Stellæ MDCLXI. SVPERIORVM PERMISSV.
[7.] COSMVM TERTIVM ETRVRIÆ PRINCIPEM. 10: AL FONSVS BORELLIVS F.
[8.] CAVE CHRISTIANE LECTOR.
[9.] IN NOMINE DEI MISERICORDIS MISERATORIS. PROOE MIVM ABALPHATHI FILII MAHMVDI, FILII ALCASEMI, FILII ALPHADHALI ASPHAHANENSIS. LAVS DEO VTRIVSQVE SECVLI DOMINO.
[10.] ABRAHAMI ECCHELLENSIS IN LATINAM EX ARABICIS Librorum Apollonij Pergæi verſionem PRÆFATIO.
[11.] PRÆFATIO AD LECTOREM.
[12.] INDEX
[13.] APOLLONII PERGAEI CONICORVM LIB. V. DEFINITIONES. I.
[14.] II.
[15.] III.
[16.] IV.
[17.] V.
[18.] VI.
[19.] VII.
[20.] VIII.
[21.] IX.
[22.] X.
[23.] XI.
[24.] XII.
[25.] XIII.
[26.] XIV.
[27.] XV.
[28.] XIV.
[29.] NOTÆ.
[30.] SECTIO PRIMA Continens propoſitiones I. II. & III. Apollonij. PROPOSITIO I.
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page |< < (233) of 458 > >|
271233Conicor. Lib. VI. parallela conſeruantur; igitur duæ ſectiones K H M, & L X S, exiſtentes in
eodem plano ſecante duas ſuperficies, quæ licet in infinitum producantur vbique
ſeparatæ ſunt, erunt aſymptoticæ.
Quartò, quia duæ hyperbolæ H K M, & L
X S ſunt æquales, ſimiles, &
ſimiliter poſitæ circa communem diametrum H X
11Prop. 7.
addit.
I, earum diſtantiæ ſemper magis, ac magis diminuuntur;
nunquam tamen mi-
nores efſici poſſunt interuallo duarum æquidiſtantium, hyperbolas continentium.
Et hoc erat propoſitum.
Data hyperbola X duos conos ſimiles exhibere vt idem planum in eis
22PROP.
13.
Addit.
efficiat duas hyperbolas ſimiles, &
æquales datæ, quæ aſymptoticæ ſint,
&
ex vna parte ſibi ipſis viciniores fiant interuallo minori quolibet da-
to:
ex altera verò parte ad ſe ipſas propius accedant interuallo tamen
maiore dato:
oportet autem vt angulus ab aſymptotis ſectionis X con-
tentus ſit acutus.
318[Figure 318]
In quolibet @l@no fiat angulus A d O æqualis angulo inclinationis diametri,
&
baſis hyperb l@ X; & per o d extenſo quolibet alio planol, ducatur in eo re-
cta linea B d C perpendicularis ad O d G, &
ſumpto quolibet alio puncto b in
recta linea G O in plano per B G C O ducto, centris d, &
b deſcribantur

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